The present invention relates to a method for generating a choice of individual photons or photon pairs in an optical channel. The invention furthermore relates to a device for implementing the method, the device being usable in particular as a controllable light source for one-photon or two-photon states and/or as a controllable separating filter or controllable gate for quantum states. The invention also relates to a network composed of a plurality of such devices.
The appearance of parametric fluorescence occurs in optically non-linear crystals. Under certain circumstances, a single energy quantum (photon) of an intensive optical pumping light source, usually a laser light source, disintegrates with a certain probability into two energy quanta or photons of approximately half the energy (H. Paul, Non-linear Optiks, vol. 2, page 94 ff, Berlin 1973). In the case of monochromatic or narrow-band excitation, the spectral distribution of the fluorescence photons is not necessarily narrow-band as well. However, because of the conservation of energy, the sum of the energies of the two fluorescence photons must be equal to the energy of the excitation photon. The same holds true for the conservation of momentum. Therefore, the parametric fluorescence only occurs when working with specific excitation geometries, i.e., given a specific alignment of the pump beam relative to the optical axes of the non-linear crystal and given specific adapted refractive indices. The result is that, depending upon the excitation geometry, the fluorescent light is emitted with two different main frequencies, i.e. wavelengths, into defined space directions relative to the direction of propagation of the pump beam. The two fluorescence photons are emitted virtually simultaneously, i.e., within a time of approximately 10. femtoseconds, and into the same or different space directions depending on the type of non-linear crystal and the excitation geometry. Their polarization direction is established in the same way. The physical properties of the two photons of the parametric fluorescence are linked to one another by a number of secondary conditions; quantum mechanically, they are in an entangled state. The entangled photons are a single state from the standpoint of quantum mechanics, in which two photons remain inseparable, it being possible to make precise statements about the physical properties of one photon using measurements on the other respective photon. Such two-photon states are of technical importance as the starting state for quantum cryptography, the optical random-sequence generator or for the quantum computer.
At present, only classical methods are known for separating the photons of a swarm from one another and coupling into different optical channels, or else jointly into a single optical channel such as a glass fiber. A familiar classical possibility for separating a plurality of photons and coupling into two different channels is, first of all, the customary beam splitter, a partially mirrored glass plate in which the mirror coating is semitransparent for the wavelength utilized, or contains small holes. The partial mirroring can also be effected by vapor-deposited thin layers. These beam splitters usually stand at an angle a in the beam path, so that a portion of the light falling on the beam splitter is deflected from the original beam direction. Another possibility for coupling out a portion of the photons of a swarm is the use of a polarizing beam splitter. Its properties are based on the principle of reflection at dielectric layers or crystal-optical prisms such as the Nicol prism.
In the event the individual photons are coherent among themselves, interference methods are also available for the beam splitting. Here, the best-known are the Michelson interferometer which transmits the constructively interfering photons and reflects the destructively interfering photons, as well as the Mach-Zehnder interferometer which sorts constructively and destructively interfering photons into two different output channels. The diffraction grating also belongs to the beam splitters operating interferometrically.
One characteristic of all these beam splitters is that the distribution of the individual photons at the beam splitter into the individual output channels can only be predicted with regard to their distribution probability. A photon pair is separated at a 1:1 dividing beam splitter with the probability of xc2xd, regardless of whether it is a question of two differentiable or two non-differentiable photons. However, it is impossible to make an exact statement as to whether a currently existing photon pair is actually separated or remains together. Therefore, the controlled transition from a two-photon state to two individual photons is not possible at present. However, the controlled generation of individual photons or photon pairs in an optical channel is important in the improvement of quantum cryptography methods, in metrology and in the development of a quantum computer.
Therefore, an object of the present invention is to specify a method for generating a choice of individual photons or photon pairs in an optical channel. The intention is also to provide a device which, while carrying out the method, can be used as a controllable light source for one-photon and two-photon states in quantum cryptography and in metrology, and as a controllable separating filter or gate for quantum states in communications networks and computing networks.
The objective is achieved in a method having the following steps:
In the first method step, a two-photon state is generated, thus a pair of quantum-mechanically correlated photons which are in an entangled state. The photon pair is preferably generated in known manner by parametric fluorescence, using an optically non-linear crystal in suitable excitation geometry, a laser preferably being used as the pumping light source. Depending on the excitation geometry and type of the non-linear crystal, the fluorescence photons leave the crystal in the same or different directions at a defined angle with respect to the direction of the exciting beam, the fluorescence photons being polarized either identically or in an orthogonally linear manner between themselves. If the frequency of the pump light is 2xcfx890, the individual photons of the photon pair have the frequencies xcfx891 and xcfx892, respectively, whereby xcfx891+xcfx892=2xcfx890.
In the next step, if the photons are emitted in a collinear manner, the photon pair is separated spatially, while retaining the quantum-mechanical correlation. This is done, for example, based on the polarization of the fluorescence photons, provided this is different, or based on the wavelength, for example, with the aid of a wavelength-selective mirror.
In the next step, in each case one photon is coupled into each optical channel. One of the channels contains a dual-beam or multi-beam interferometer with a variable optical path-length difference xcex41Fxe2x88x92xcex41S; the other channel contains an optical delay section having the optical length xcex41. Both channels are reunited again through a beam splitter. The optical channels have the same basic length, understood by this being the optical distance of the location at which the photons of the photon pair are spatially separated, to the beam divider, i.e. to the detectors when passing through the respective beam-component paths; in the case of the beam path with interferometer, the length determined via the interferometer arms. The optical paths covered in the interferometer and in the optical delay section, respectively, must be taken into account when determining the basic length.
The interferometer utilized in one of the optical channels is a two-beam interferometer such as a Mach-Zehnder or a Michelson interferometer, or a multi-beam interferometer such as a Fabry-Perot interferometer, or an Echelon. In this context, it is essential that the optical path difference xcex41Fxe2x88x92xcex41S be adjustable over at least one half of an average wavelength xcex of the fluorescence photons. In addition, the interferometer can be a linearly birefringent crystal plate, particularly a quartz plate, whose optical path difference is enlarged by an additional compensator, such that the path difference can be adjusted by more than one half wavelength xcex1 of those photons which are passing through the interferometer.
The optical delay section arranged in the other channel is preferably variable in the same way as the optical path-length difference in the interferometer. The optical delay section is preferably implemented by an optical xe2x80x9ctrombone slidexe2x80x9d or by an electro-optical element whose refractive index is variable, making it possible to induce a variable phase difference. Furthermore, the indicated delay section can also be composed of a delay section of fixed length and an adjustment element which is able to introduce a variable phase difference corresponding approximately to one half of an average wavelength. However, the optical delay section does not necessarily have to be variable.
In the next method step, variables xcex41F, xcex41S and xcex41 are adjusted such that the probability K for coincidences between the outputs of the beam splitter is a choice of approximately K=0 or K=1, or approximately a predetermined intermediate value. Probability K is proportional to the coincidence rate which can easily be determined by arranging one detector at each output of the beam splitter and determining the coincidence rate between both outputs in known manner by evaluating the counter totals. A coincidence probability of zero corresponds to the case when both photons of the originally generated photon pair are emitted in a shared output channel of the beam splitter, thus are emitted in a collinear manner. In this context, it is uncertain which of the two output channels the photon pair takes. The probability for a specific channel is in each case 50%. On the other hand, a maximum coincidence rate, corresponding to K≈1, is obtained for the case when both photons arrive in different output channels of the beam splitter, and thus there is only one photon per output channel.
One or more mechanical and/or electro-optical adjustment elements, which preferably can be controlled remotely, are provided for changing optical path lengths xcex41F, xcex41S and/or xcex41. For example, the mechanical adjustment elements are mirrors which are displaceable by a motor. However, electronically controllable liquid-crystal cells and/or electro-optical crystal modulators are advantageous, especially for adjusting the phase in the interferometer. The phase is adjusted with liquid crystals in microseconds, even in nanoseconds with the aid of electro-optical crystal modulators. A rapid and precise adjustment of the phase between two predetermined values is particularly interesting for the case when the intention is to switch over quickly between one or two photons in the output channel.
Preferably the optical path-length difference in the interferometer (xcex41Fxe2x88x92xcex41S) is so adjusted that it amounts to an integral multiple of the half average wavelength xcex0 of the photons of the photon pair, thus |xcex41Fxe2x88x92xcex41S|=n/2 xcex0, where n=0, 1, 2 . . . At the same time, optical length xcex41 of the delay section is adjusted to the average path difference xc2xd (xcex41F+xcex41S) of the interferometer. Only photon pairs or individual photons are generated in the output channel, depending upon whether the optical path-length difference in the interferometer is an even-numbered or odd-numbered multiple of half wavelength xcex0. The transition from n to nxc2x11 corresponds to the transition from K≈0 to K≈1, or vice versa. Since the adjustment of the device for non-linear crystals of type I and II, respectively, is somewhat different from one another, the setting of optical lengths xcex41F, xcex41S and xcex41 is preferably checked experimentally, by measuring the coincidence rate.
The device can also be adjusted completely experimentally by determining the probability K for coincidences between the outputs of the beam splitter as a function of variables xcex41F, xcex41S and/or xcex41. In so doing, the settings of the optical lengths resulting in K≈0 and/or K≈1 and/or a predetermined intermediate value are recorded in each case, so that it is possible to switch over between individual photons and photon pairs in the output channel by switching over between recorded values for the corresponding lengths, i.e. between the corresponding settings of the adjustment elements.